5-Minute Check on Chapter 2 Transparency 3-1 Click the mouse button or press the Space Bar to display the answers. 1.Evaluate 42 - |x - 7| if x = -3 2.Find 4.1  (-0.5) Simplify each expression 3. 8(-2c + 5) + 9c 4. (36d – 18) / (-9) 5.A bag of lollipops has 10 red, 15 green, and 15 yellow lollipops. If one is chosen at random, what is the probability that it is not green? 6. Which of the following is a true statement Standardized Test Practice: ACBD 8/4 < 4/8-4/8 < -8/4-4/8 > -8/4-4/8 > 4/8

Lesson 9-6 Perfect Squares and Factoring

Transparency 6 Click the mouse button or press the Space Bar to display the answers.

Transparency 6a

Objectives Factor perfect square trinomials Solve equations involving perfect squares

Vocabulary Perfect square- a number whose square root is a rational number trinomial– the sum of three monomials

Factoring Perfect Square Trinomials If a trinomial can be written in the form: a 2 + 2ab + b 2 or a 2 – 2ab + b 2 then it can be factored as (a + b) 2 or as (a – b) 2 respectively Symbols: a 2 + 2ab + b 2 = (a + b) 2 or a 2 – 2ab + b 2 = (a – b) 2 Examples: x 2 + 6x + 9 = (x + 3) 2 4x 2 – 24x + 36 = (2x – 6) 2

Example 1a Determine whether is a perfect square trinomial. If so, factor it. Answer:is a perfect square trinomial. 3. Is the middle term equal to? Yes, 1. Is the first term a perfect square? Yes, 2. Is the last term a perfect square?Yes, Write as Factor using the pattern.

Example 1b Determine whether is a perfect square trinomial. If so, factor it. 1. Is the first term a perfect square? Yes, 2. Is the last term a perfect square?Yes, 3. Is the middle term equal to? No, Answer:is not a perfect square trinomial.

Example 2a Factor. First check for a GCF. Then, since the polynomial has two terms, check for the difference of squares. 6 is the GCF. and Factor the difference of squares. Answer:

Example 2b Factor. This polynomial has three terms that have a GCF of 1. While the first term is a perfect square, the last term is not. Therefore, this is not a perfect square trinomial. This trinomial is in the formAre there two numbers m and n whose product is and whose sum is 8 ? Yes, the product of 20 and –12 is –240 and their sum is 8.

Example 2b cont Write the pattern and Group terms with common factors Factor out the GCF from each grouping is the common factor. Answer:

Example 3 Solve Recognize as a perfect square trinomial. Original equation Factor the perfect square trinomial. Set the repeated factor equal to zero. Solve for x. Answer: Thus, the solution set isCheck this solution in the original equation.

Example 4a Solve. Original equation Square Root Property Add 7 to each side. Simplify. Separate into two equations. or Answer: The solution set isCheck each solution in the original equation.

Example 4b Solve. Original equation Recognize perfect square trinomial Factor perfect square trinomial Square Root Property Subtract 6 from each side. Answer: The solution set is or Separate into two equations. Simplify.

Example 4c Solve. Original equation Square Root Property Subtract 9 from each side. Answer: Since 8 is not a perfect square, the solution set is Using a calculator, the approximate solutions areor about –6.17 and or about –11.83.

Example 4c cont Check You can check your answer using a graphing calculator. GraphandUsing the INTERSECT feature of your graphing calculator, find whereThe check of –6.17 as one of the approximate solutions is shown.

Factoring Techniques Greatest Common Factor (GCF) Factor out a Common Factor Difference of Squares Perfect Square Trinomials Factoring by Grouping

Summary & Homework Summary: –If a trinomial can be written in the form a 2 + 2ab + b 2 or a 2 – 2ab + b 2, then it can be factored as (a + b) 2 or (a – b) 2, respectively –For a trinomial to be factorable as a perfect square, the first term must be a perfect square, the middle must be twice the product of the square roots of the first and last terms, and the last term must be a perfect square –Square Root Property: for any number n>0, if x 2 = n, then x = +- √n Homework: –Pg ,26-38,44,46